Jacobi Fields and Tidal Effects in Kerr Spacetime

TL;DR

This paper derives and analyzes tidal equations and Jacobi fields in Kerr spacetime, focusing on the rest frame of a Kerr source and implications for astrophysical jets.

Contribution

It formulates relativistic tidal equations in Kerr spacetime and explores Jacobi fields within Fermi coordinates for observers at rest, linking to astrophysical jet phenomena.

Findings

Tidal equations are explicitly formulated for Kerr spacetime.

Solutions of Jacobi equations are connected to jet phenomena.

Rest frame of Kerr source is characterized in detail.

Abstract

General relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source described by the Kerr gravitational field. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The generalized Jacobi equation for the free motion of a test particle is worked out within the Fermi coordinate system established along the world line of a fiducial observer at rest on the symmetry axis of the exterior Kerr background. The nature of the solutions of these equations are investigated in connection with the phenomena associated with astrophysical jets.